Comparing fractions

In introduction to Fractions, us learned that fractions space a means of mirroring part the something. Fractions are useful, due to the fact that they let us tell exactly how much we have of something. Some fractions are bigger than others. Because that example, i beg your pardon is larger: 6/8 the a pizza or 7/8 of a pizza?

In this image, we have the right to see that 7/8 is larger. The illustration provides it straightforward to compare these fractions. Yet how can we have actually done it there is no the pictures?

Click through the slideshow come learn how to to compare fractions.

You are watching: Is 1/2 bigger than 1/4

Earlier, we witnessed that fractions have actually two parts.

One component is the height number, or numerator.

The various other is the bottom number, or denominator.

The denominator tells us how numerous parts room in a whole.

The numerator tells united state how numerous of those parts we have.

When fractions have actually the very same denominator, it method they're break-up into the same variety of parts.

This means we can compare these fractions simply by looking in ~ the numerator.

Here, 5 is much more than 4...

Here, 5 is much more than 4...so we have the right to tell that 5/6 is more than 4/6.

Let's look at at an additional example. I m sorry of this is larger: 2/8 or 6/8?

If you thought 6/8 was larger, you were right!

Both fractions have the same denominator.

So we compared the numerators. 6 is bigger than 2, for this reason 6/8 is an ext than 2/8.

As girlfriend saw, if two or more fractions have actually the very same denominator, you can compare them by feather at their numerators. As you can see below, 3/4 is bigger than 1/4. The bigger the numerator, the larger the fraction.

Comparing fractions with various denominators

On the vault page, we contrasted fractions that have the very same bottom numbers, or denominators. But you know that fractions have the right to have any number together a denominator. What happens as soon as you must compare fountain with different bottom numbers?

For example, i m sorry of this is larger: 2/3 or 1/5? It's difficult to tell simply by looking at them. After ~ all, 2 is bigger than 1, but the denominators aren't the same.

If girlfriend look in ~ the picture, though, the distinction is clear: 2/3 is larger than 1/5. With an illustration, the was easy to compare these fractions, however how might we have done it there is no the picture?

Click with the slideshow to learn exactly how to compare fractions with various denominators.

Let's to compare these fractions: 5/8 and 4/6.

Before us compare them, we need to change both fractions so they have the very same denominator, or bottom number.

First, we'll uncover the smallest number that have the right to be separated by both denominators. We contact that the lowest typical denominator.

Our first step is to find numbers that deserve to be split evenly by 8.

Using a multiplication table provides this easy. All of the numbers on the 8 row have the right to be separated evenly through 8.

Now let's look in ~ our 2nd denominator: 6.

We have the right to use the multiplication table again. All of the number in the 6 row can be split evenly by 6.

Let's to compare the two rows. It looks choose there room a couple of numbers that can be divided evenly by both 6 and 8.

24 is the the smallest number that appears on both rows, so it's the lowest typical denominator.

Now we're walk to change our fractions so they both have actually the very same denominator: 24.

To carry out that, we'll have to adjust the numerators the same way we changed the denominators.

Let’s look at 5/8 again. In stimulate to change the denominator to 24...

Let’s look at 5/8 again. In bespeak to readjust the denominator to 24...we had to main point 8 through 3.

Since we multiplied the denominator through 3, we'll likewise multiply the numerator, or peak number, by 3.

5 times 3 equates to 15. For this reason we've readjusted 5/8 right into 15/24.

We deserve to do the because any type of number end itself is same to 1.

So once we multiply 5/8 by 3/3...

So once we multiply 5/8 by 3/3...we're yes, really multiplying 5/8 by 1.

Since any kind of number times 1 is equal to itself...

Since any type of number time 1 is equal to itself...we can say the 5/8 is same to 15/24.

Now we'll perform the very same to our other fraction: 4/6. Us also adjusted its denominator come 24.

Our old denominator was 6. To gain 24, we multiplied 6 through 4.

So we'll likewise multiply the molecule by 4.

4 time 4 is 16. Therefore 4/6 is equal to 16/24.

Now that the denominators room the same, we deserve to compare the two fractions by feather at their numerators.

16/24 is bigger than 15/24...

16/24 is bigger than 15/24... For this reason 4/6 is bigger than 5/8.

Rchrischona2015.orgcing fractions

Which of these is larger: 4/8 or 1/2?

If friend did the math or also just looked in ~ the picture, you might have been able to tell the they're equal. In other words, 4/8 and also 1/2 typical the same thing, even though they're created differently.

If 4/8 method the exact same thing together 1/2, why not just speak to it that? One-half is easier to say 보다 four-eighths, and for most world it's likewise easier come understand. After all, as soon as you eat out v a friend, you separation the bill in half, no in eighths.

If you compose 4/8 together 1/2, you're rchrischona2015.orgcing it. Once we rchrischona2015.orgce a fraction, we're creating it in a simpler form. Rchrischona2015.orgced fractions are always equal to the initial fraction.

We already rchrischona2015.orgced 4/8 to 1/2. If girlfriend look in ~ the examples below, you deserve to see that various other numbers deserve to be rchrischona2015.orgced come 1/2 together well. This fractions are all equal.

5/10 = 1/211/22 = 1/236/72 = 1/2

These fractions have actually all to be rchrischona2015.orgced to a simpler type as well.

4/12 = 1/314/21 = 2/335/50 = 7/10

Click through the slideshow come learn exactly how to rchrischona2015.orgce fountain by dividing.

Let's try rchrischona2015.orgcing this fraction: 16/20.

Since the numerator and also denominator space even numbers, you have the right to divide castle by 2 to rchrischona2015.orgce the fraction.

First, we'll divide the molecule by 2. 16 divided by 2 is 8.

Next, we'll divide the denominator by 2. 20 divided by 2 is 10.

We've rchrischona2015.orgced 16/20 to 8/10. We could also say that 16/20 is equal to 8/10.

If the numerator and denominator deserve to still be separated by 2, us can continue rchrischona2015.orgcing the fraction.

8 divided by 2 is 4.

10 split by 2 is 5.

Since there's no number the 4 and 5 can be divided by, we can't rchrischona2015.orgce 4/5 any further.

This method 4/5 is the simplest form of 16/20.

Let's shot rchrischona2015.orgcing one more fraction: 6/9.

While the numerator is even, the denominator is an odd number, so we can't rchrischona2015.orgce by splitting by 2.

Instead, we'll need to uncover a number the 6 and also 9 have the right to be divided by. A multiplication table will certainly make that number simple to find.

Let's uncover 6 and also 9 on the same row. As you can see, 6 and also 9 can both be separated by 1 and also 3.

Dividing by 1 won't readjust these fractions, for this reason we'll usage the largest number that 6 and 9 have the right to be divided by.

That's 3. This is called the greatest usual divisor, or GCD. (You can additionally call it the greatest common factor, or GCF.)

3 is the GCD that 6 and also 9 because it's the largest number they can be separated by.

So we'll divide the numerator by 3. 6 separated by 3 is 2.

Then we'll division the denominator by 3. 9 split by 3 is 3.

Now we've rchrischona2015.orgced 6/9 come 2/3, i m sorry is its simplest form. Us could additionally say that 6/9 is equal to 2/3.

Irrchrischona2015.orgcible fractions

Not all fractions can be rchrischona2015.orgced. Some are currently as an easy as they can be. For example, friend can't rchrischona2015.orgce 1/2 because there's no number various other than 1 that both 1 and 2 have the right to be separated by. (For the reason, friend can't rchrischona2015.orgce any portion that has actually a molecule of 1.)

Some fractions that have actually larger number can't be rchrischona2015.orgced either. Because that instance, 17/36 can't it is in rchrischona2015.orgced since there's no number that both 17 and also 36 deserve to be divided by. If girlfriend can't find any type of common multiples for the number in a fraction, opportunities are it's irrchrischona2015.orgcible.

Try This!

Rchrischona2015.orgce each portion to its simplest form.

Mixed numbers and improper fractions

In the previous lesson, you learned about mixed numbers. A blended number has both a fraction and a whole number. An instance is 1 2/3. You'd read 1 2/3 choose this: one and also two-thirds.

Another method to write this would certainly be 5/3, or five-thirds. These 2 numbers watch different, yet they're actually the same. 5/3 is one improper fraction. This just method the numerator is larger than the denominator.

There are times once you might prefer to usage an improper fraction instead of a combined number. It's basic to adjust a blended number right into an not correct fraction. Let's find out how:

Let's convert 1 1/4 into an wrong fraction.

First, we'll require to discover out how plenty of parts consist of the entirety number: 1 in this example.

To carry out this, we'll multiply the whole number, 1, by the denominator, 4.

1 time 4 amounts to 4.

Now, let's include that number, 4, to the numerator, 1.

4 to add 1 equals 5.

The denominator remains the same.

Our improper portion is 5/4, or five-fourths. Therefore we can say that 1 1/4 is same to 5/4.

This method there are five 1/4s in 1 1/4.

Let's convert an additional mixed number: 2 2/5.

First, we'll multiply the entirety number by the denominator. 2 time 5 amounts to 10.

Next, we'll include 10 come the numerator. 10 add to 2 amounts to 12.

As always, the denominator will stay the same.

So 2 2/5 is equal to 12/5.

Try This!

Try convert these blended numbers into improper fractions.

Converting not correct fractions into mixed numbers

Improper fractions are valuable for math troubles that usage fractions, together you'll find out later. However, they're also more complicated to read and also understand than mixed numbers. Because that example, it's a lot simpler to picture 2 4/7 in your head 보다 18/7.

Click through the slideshow come learn exactly how to readjust an improper fraction into a mixed number.

Let's revolve 10/4 into a combined number.

You have the right to think the any fraction as a division problem. Just treat the line in between the numbers choose a division sign (/).

So we'll divide the numerator, 10, through the denominator, 4.

10 split by 4 equates to 2...

10 divided by 4 equals 2... Through a remainder that 2.

The answer, 2, will end up being our totality number because 10 deserve to be split by 4 twice.

And the remainder, 2, will come to be the molecule of the portion because we have actually 2 parts left over.

The denominator continues to be the same.

So 10/4 equals 2 2/4.

Let's try another example: 33/3.

We'll division the numerator, 33, by the denominator, 3.

33 separated by 3...

33 separated by 3... Equals 11, through no remainder.

The answer, 11, will become our entirety number.

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There is no remainder, so we have the right to see the our improper portion was actually a entirety number. 33/3 equals 11.